1.3.1 Cold gas thruster
The cold gas thruster is the simplest form of propulsion. An inert propellant gas is stored in a pressurised vessel aboard a spacecraft. When required, a valve releases the propellant, which flows through a nozzle and exits into space.
Momentum is being carried off by the escaping propellant. The rate of change of mo- mentum p˙ is given by:
˙ p= d
dt(muex) = ˙muex (1.1)
wherem˙ is the mass flow rate of the propellant anduexis the velocity at which the propellant exits the thruster, with the assumption of an ideal case where uex is uniform across the thruster exit. By Newton’s second law of motion, a nonzerop˙is equivalent to a nonzero force acting on the propellant. If that is the case, then Newton’s third law of motion necessitates a force equal in magnitude but opposite in direction that acts on the thruster. Assuming ideal nozzle expansion, then the instantaneous thrust forceFtacting on a spacecraft of total massM including its onboard propellant is:
Ft=−m˙uex =Mv˙ (1.2)
which accelerates the spacecraft atv˙ in the direction opposite touex.
On a spacecraft, M and m˙ are limited by mission specifications and propellant budget. The only other way to obtain higherFt=|Ft|is by increasinguex =|uex|which is primarily
dependent on temperature and the nature by which the propellant is accelerated. In a cold gas thruster the only means of accelerating propellant is by using a converging-diverging nozzle. The convergent section accelerates subsonic flow up to the local sound speed cs at the nozzle throat. For an ideal gas:
cs= r
γkBT
m (1.3)
whereγ is the gas adiabatic index,kB is the Boltzmann constant, m is the molecular mass of the gas, and T is the temperature of the propellant. Since the propellant is not heated, cs is low. The divergent section then accelerates the sonic flow to supersonic velocities, but
the increase in velocity is fixed by the geometry of the nozzle and also dependent on other factors such as temperature, pressure, and boundary layer frictional losses. Consequently,
uex is ultimately limited by cs. As such, Ft produced by cold gas thrusters is typically in the∼µN to ∼mN range, scaling roughly linearly withm˙.
The specific impulse Isp is a convenient measure of thruster effectiveness, defined as
the change in momentum delivered per unit mass of propellant. From an experimental perspective using measurable parameters:
Isp= uex
g0 (1.4)
whereg0 is the standard gravity. The relation is independent ofm˙, and solely dependent on
uex. From a theoretical perspective, the maximum specific impulse Iˆsp a gas can achieve is given by the thermodynamic relation:
ˆ Isp= 1 g0 v u u tkBTst m 2γ γ−1 " 1− pex pst γ−γ1# (1.5) The whole term after the1/g0 prefix represents the theoretical maximum velocityuˆex of the propellant exiting from the thruster [40], where Tst andpst are the stagnation temperature and pressure respectively taken upstream of the nozzle, andpexis the pressure at the thruster exit. Assumingpex = 0Torr for ideal vacuum expansion, Iˆsp becomes dependent only onTst
andm. For a cold gas thruster operating with inert gas propellants such as argon, xenon, or
nitrogen at a fixedTst= 300K, the respective values are Iˆsp(Ar) = 57.0s, Iˆsp(Xe) = 31.4s, and Iˆ
sp(N2) = 80.5s. In practice however, the actual Isp achieved can be significantly less thanIˆ
sp due to boundary layer frictional losses and nonideal expansion.
1.3.2 Chemical propellant thruster
A straightforward way to increaseIsp is by raising the temperature of the propellant. Warm
gas and chemical propellant thrusters commonly use monopropellants such as hydrazine (N2H4) and hydrogen peroxide (H2O2). The propellant is catalytically decomposed in an exothermic reaction, whereby the release of chemical energy heats the propellant to temper- atures up to ∼ 1000K. Bi- or tripropellant systems also exist but have increased system complexity and cost. Chemical propellant thrusters are able to produceFt from ∼mN up
to∼N, withIˆsp on the order of ∼100s. However, it is difficult to finely manipulate thrust from chemical propellant thrusters for precision manoeuvres and attitude control, which limits their applications to ballistic trajectories.
While better performing than a cold gas thruster, the flammability and toxicity of chem- ical propellants result in higher costs in ground handling and propellant loading procedures, and may require a significant portion of a microspacecraft mission financial budget. Addi- tionally, the operational lifetime of a chemical propellant thruster is limited by the lifetime of the catalyst which is prone to degradation and failure over time.
1.3.3 Resistojet
If hazardous chemical propellants are not desirable, then an inert propellant may heated electrically using a resistive heating element. In a resistojet, propellant flowing past the surface of the heating element is heated via conduction and convection, and then thermally expanded through a nozzle. Propellant options include water (H2O) and nitrous oxide (N2O) but chemical propellants like butane (C4H10) and N2H4 are also compatible.
The main drawback of a resistojet is the long warm up time of the heating element which means that thrust production is suboptimal before thermal equilibrium is attained. Furthermore, thermal conductance to a gas propellant is inefficient, and a significant amount of the thermal energy is sunk into the thermally insulating walls of the thruster. A resistojet has similar performance as a chemical propellant thruster, withFt production on the∼mN
to ∼ N scale, and Iˆsp on the order of ∼ 100s, scaling with power. Resistojets typically operate with ∼kW of electrical power. Their use on microspacecraft missions with limited
power budgets requires the development of miniaturised low power versions of the current resistojet technologies [5].
1.3.4 Arcjet
An arcjet is an electrothermal thruster whereby propellant is heated using a direct current (DC) arc discharge. The design of an arcjet typically consists of a nozzle-shaped anode wall and a cathode spike located slightly upstream of the nozzle throat, around which propellant is flowed in a swirl pattern. High voltage & kV pulses are sent to the cathode spike until breakdown is initiated in the surrounding propellant, after which a low voltage at high current sustains the arc discharge. Outside of the arc, the degree of ionisation is small, and plasma effects may be neglected when considering the flow behaviour of the propellant at the nozzle exit.
Arcjets typically use inert propellants, but extra energy may be extracted from chemically reactive propellants like N2H4. Propellant flowing through the arc volume is heated to tem- peratures exceeding∼1000K. The volumetric heating process is more effective than surface heating, and less thermal energy is lost to the thruster walls. However, plasma ignition and the transition to steady state must be carefully and reliably controlled to minimise damage and wear to the exposed thruster walls. Most arcjets operate at powers above ∼1kW but there is interest in the development of.100W arcjets for use on microspacecraft [6,7]. Low power arcjets can attainIˆ
sp on the order of∼100s but the value can be a few times higher at ∼kW levels, and likewise achieveFt on the scale of∼mN up to ∼N.
1.3.5 Hollow cathode thruster
There are four main components in a hollow cathode thruster. A heating element surrounds a hollow refractory cathode tube which contains an insert made from a low work function material. These three components are enclosed by a keeper electrode. An inert propellant like Ar or Xe is flowed through the cathode tube. The insert is heated to temperatures required for thermionic emission, producing electrons which ionise the propellant. Initial breakdown is facilitated by the keeper electrode which is biased positively relative to the cathode. A restrictive orifice plate or nozzle at the end of the cathode tube contains the plasma at a high pressure. The plasma volumetrically heats the propellant which exits through the orifice or nozzle to produce thrust. During plasma operation, the insert is also heated by the hot propellant, high energy electrons, and ion bombardment. If there is sufficient thermal energy deposited to maintain the thermionic emission temperature of the insert, a hollow cathode thruster can function in a ‘self-heating’ mode, whereby the heating element is no longer required and can be turned off to conserve power. Heater-less hollow cathode thrusters also exist, but require an ignition phase to achieve plasma breakdown, followed by a plasma-induced heating phase prior to regular operation [11,12].
The lifetime of a hollow cathode thruster is severely limited by the susceptibility of the insert to contamination, as well as the eventual erosion of the insert and keeper electrode due to sputtering and bombardment of high energy ions. Presence of energetic ions in the exhaust plume may also result in sputtering and contamination of solar panels and other surfaces on the exterior of the spacecraft [22]. Like the resistojet, a hollow cathode thruster is also subjected to long warm up times, but it is able to divert the thermal energy loss from the hot propellant to heating the insert for more efficient operation. A hollow cathode thruster has similar advantages as the arcjet in terms of volumetric heating of the propellant, and is able to achieve similar performance with Ft on the ∼mN scale andIˆsp on the order
of∼100s with .100W of power [9,10].
1.3.6 Pocket Rocket
Pocket Rocket (henceforth abbreviated asPR) is a radiofrequency plasma electrothermal mi- crothruster currently under active development by the Space Plasma, Power and Propulsion (SP3) Laboratory at The Australian National University, Canberra [15,16,41,42].
PR, along with the propellant [43–45] and RF power [46,47] subsystems, are being designed and tested for deployment on the CubeSat platform [16].
At the core of PR is an annular electrode fitted coaxially around the outside of a hollow refractory tube discharge chamber [13]. PRcan operate with a wide range of gas propellants but performs best with monatomic inert gas propellants such as Ar and Xe. A weakly ionised plasma is ignited in the propellant flowing through the discharge chamber with .10W of radiofrequency (RF) power supplied to the electrode [14, 48]. The propellant is heated volumetrically via ion-neutral charge exchange collisions [14, 49, 50]. At low power and on short time scales, heating in the plasma bulk dominates, and the temperature of the propellant peaks in the middle of the discharge [50]. At high power and on long time scales, heating in the plasma sheath dominates, and the temperature of the propellant peaks near the discharge chamber wall instead [51,52]. Operating at low power minimises the conductive losses to the discharge chamber wall; thermal energy is retained in the propellant, which is beneficial for thrust. PRis able to achieveFt on the order of∼1mN [48,53], scaling withm˙ and RF power. Like the other electrothermal thrusters, Iˆ
sp is on the order of ∼100s, and scales with RF power.
An advantage of thePRRF discharge over DC discharges like arcjets and hollow cathode thrusters is its ability to initiate plasma breakdown in a smaller volume and at lower voltages. In the presence of an electric field set up by an applied voltage, electrons are accelerated and subsequently undergo ionising collisions with the background neutral gas medium. Each ion- ising collision creates an ion-electron pair, resulting in an ‘electron avalanche’ characterised by an exponential growth of the electron number densityne:
ne=ne,0exp d λi (1.6) where ne,0 is the initial electron population, λi is the ionisation mean free path, and d
is the path length travelled by the electron avalanche [54]. Breakdown occurs when ne
surpasses a sufficiently high threshold for the medium to become electrically conductive, and a stable plasma is sustained when the creation and loss of charged plasma species are at equilibrium. During breakdown, ne is limited by d, which in the case of a DC discharge is
the distance between the cathode and the anode along the unidirectional DC electric field. In a RF discharge on the other hand, the alternating electric field causes electrons to oscillate within the medium, thereby extending the path length of the electron avalanche before it terminates at an electrode or wall. The increase indeffectively magnifies the electric field,
thus allowing breakdown to initiate at a lower applied voltage, and the breakdown threshold is also surpassed more quickly given the exponential growth ofne.
Plasma breakdown in PR can be initiated at RF voltages as low as ∼ 100V [42], and occurs almost instantaneously on a ∼ µs time scale [55]. Unlike hollow cathode thrusters
and arcjets, there is no warm up time and high voltage arcs are not required for plasma ignition. The propellant reaches target temperatures of up to ∼ 1000K on a time scale of ∼100ms [50, 55], which allows PR to operate with rapid pulsing of both the propellant flow and RF power. The discharge chamber wall in PRis heated by ion bombardment, and thermal equilibrium with the propellant is attained on a time scale of ∼ 10s [50, 51, 55]. Higher performance can be achieved during continuous operation on this time scale as the discharge chamber wall acts as a source of thermal energy for the propellant in addition to the volumetric plasma-induced heating [52].
Another compelling design feature of PR is the shielding of the RF powered electrode from the plasma by discharge chamber wall. As such, ion bombardment onto the refractory discharge chamber wall is not a concern, unlike the exposed metallic anode in an arcjet or the unprotected insert and keeper electrode in a hollow cathode thruster. On the contrary, because PR is a ‘gamma mode’ discharge [56] sustained mainly by secondary electrons (as opposed to an ‘alpha mode’ discharge sustained mainly by primary electrons in the plasma bulk [57]), ion bombardment is in fact favourable since it facilitates the emission of high energy secondary electrons from the discharge chamber wall.
Further improvements are made to the design of PR to confine the plasma within the discharge chamber, thereby releasing an essentially neutral exhaust plume with a very low electric potential. This prevents the contamination of externally mounted solar panels by a return ion current, as well as electrical interference with sensitive instruments [48].